rotating edge loops individually on their own axis
It's all about the setup.


model your flower and delete all the rest of the petals leaving one.
since there is 5 sides each petals need to rotate 72 degree.
Using array modifier with a rotated empty I reconstructed the flower.
Now I can modify one petal to make sure all the rest of the petals follow.


Here is the blend file I created ...


Select edit mode.
Select edge mode.
Make sure to select the edge you want to rotate from last (The Active Element)
Set pivot point to "Active Element"
Hit N to open navigation panel in 3d view.
Look for Transform Orientation tab.
Hit the "+" button to setup Transform Orientation to the face you want to rotate.
Remember to choose from the list of newly created Transform Orientation called "face" if there are more than one it should look like "face.001 or face.002"
Activate rotation and hit Y to rotate in the Y axis.